Derong Kong

activity

20182026

most citedThe

β

-transformation with a hole at

0

: the general case

1 citations · 2 across the 8 of their papers we have counts for

collaborators

9 papers

math.DS2026

Asymptotic separation of periodic orbits and fractal dimension

Derong Kong, Zhiqiang Wang, Daohua Yu

For a totally bounded metric dynamical system $(X, d, T)$ we introduce a new critical value $s (X, d, T)$ which quantifies the asymptotic separation of periodic orbits. Mo…

math.DS2025

Open dynamical systems with a moving hole

Derong Kong, Beibei Sun, Zhiqiang Wang

Given an integer $b \geq 3$ , let $T_{b} : [0, 1) \to [0, 1); x \mapsto b x (mod 1)$ be the expanding map on the unit circle. For any $m \in N$ and $ω=ω^0ω^1\ldots\in(\left\{0,1,\ldots,…

math.CA2025

Rational points in Cantor sets and spectral eigenvalue problem for self-similar spectral measures

Derong Kong, Kun Li, Zhiqiang Wang

Given $q \in N_{\geq 3}$ and a finite set $A \subset Q$ , let $K (q, A) = {i = 1 \sum \infty \frac{a _{i}}{q ^{i}} : a_{i} \in A \forall i \in N} .$ For…

math.DS2024★ 1 cited

The $β$ -transformation with a hole at $0$ : the general case

Pieter Allaart, Derong Kong

Given $β > 1$ , let $T_{β}$ be the $β$ -transformation on the unit circle $[0, 1)$ , defined by $T_{β} (x) = β x - ⌊ β x ⌋$ . For each $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set consist…

math.DS2024★ 1 cited

On the strong separation condition for self-similar iterated function systems with random translations

Simon Baker, Derong Kong, Zhiqiang Wang

Given a self-similar iterated function system $Φ = {ϕ_{i} (x) = ρ_{i} O_{i} x + t_{i}}_{i = 1}^{m}$ acting on $R^{d}$ , we can generate a parameterised family of iterated function systems b…

math.CA2023

Fractal Sumset Properties

Derong Kong, Zhiqiang Wang

In this paper we introduce two notions of fractal sumset properties. A compact set $K \subset R^{d}$ is said to have the Hausdorff sumset property (HSP) if for any $\ell\in\ma…

math.DS2023

Entropy plateaus, transitivity and bifurcation sets for the $β$ -transformation with a hole at $0$

Pieter Allaart, Derong Kong

Given $β > 1$ , let $T_{β}$ be the $β$ -transformation on the unit circle $[0, 1)$ such that $T_{β} (x) = β x (mod 1)$ . For each $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set consisting of all $x…

math.DS2023

On the union of homogeneous symmetric Cantor set with its translations

Derong Kong, Wenxia Li, Zhiqiang Wang +2

Fix a positive integer $N$ and a real number $0 < β < 1/ (N + 1)$ . Let $Γ$ be the homogeneous symmetric Cantor set generated by the IFS $$ \Big\{ ϕ_i(x)=βx + i \frac{1-β}{N}: i=0,1,\cdo…

math.DS2018

On the complexity of the set of codings for self-similar sets and a variation on the construction of Champernowne

Simon Baker, Derong Kong

Let $F = {p_{0}, \dots, p_{n}}$ be a collection of points in $R^{d} .$ The set $F$ naturally gives rise to a family of iterated function systems consisting of co…